Problem: Naoya read a book cover to cover in a single session, at a rate of $55$ pages per hour. After reading for $4$ hours, he had $330$ pages left to read. How long is the book?
Solution: Naoya read $55$ pages per hour, so he read $55T$ pages in $T$ hours. The total number of pages is comprised of the number of pages Naoya had already read and the number of pages that remained. We can express this with the equation $B=55T+R$, where: $B$ represents the book's length $T$ represents the time (in hours) $R$ represents the number of remaining pages to read at a given time We know that after reading for $4$ hours $(T={4})$, Naoya had $330$ remaining pages to read $(R={330})$. Let's plug these values into the equation to find the value of $B$. $ B=55\cdot{4}+{330}=550$ Therefore, the book is $550$ pages long. To find how long it took Naoya to finish the entire book, we can plug $R=0$ into the equation and solve for $T$. $ \begin{aligned}550&=55T+0\\ 55T&=550\\ T&=10\end{aligned}$ The book is $550$ pages long. It took Naoya $10$ hours to read the entire book.